Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.
J Chem Phys. 2018 Feb 21;148(7):074111. doi: 10.1063/1.5019221.
The quantum phenomenon of above barrier reflection is investigated from a time-dependent perspective using Gaussian wavepackets. The transition path time distribution, which in principle is experimentally measurable, is used to study the mean flight times ⟨t⟩ and ⟨t⟩ associated with the reflection and the transmission over the barrier paying special attention to their dependence on the width of the barrier. Both flight times, and their difference Δt, exhibit two distinct regimes depending on the ratio of the spatial width of the incident wavepacket and the length of the barrier. When the ratio is larger than unity, the reflection and transmission dynamics are coherent and dominated by the resonances above the barrier. The flight times ⟨t⟩ and the flight time difference Δt oscillate as a function of the barrier width (almost in phase with the transmission probability). These oscillations reflect a momentum filtering effect related to the coherent superposition of the reflected and transmitted waves. For a ratio less than unity, the barrier reflection and transmission dynamics are incoherent and the oscillations are absent. The barrier width which separates the coherent and incoherent regimes is identified analytically. The oscillatory structure of the time difference Δt as a function of the barrier width in the coherent regime is absent when considered in terms of the Wigner phase time delays for reflection and transmission. We conclude that the Wigner phase time does not correctly describe the temporal properties of above barrier reflection. We also find that the structure of the reflected and transmitted wavepackets depends on the coherence of the process. In the coherent regime, the wavepackets can have an overlapping peak structure, but the peaks are not fully resolved. In the incoherent regime, the wavepackets split in time into distinct separated Gaussian like waves, each one reflecting the number of times the wavepacket crosses the barrier region before exiting. A classical Wigner approximation, using classical trajectories which upon reaching an edge of the barrier are reflected or transmitted as if the edge was a step potential, is quantitative in the incoherent regime. The implications of the coherence observed on resonance reactive scattering are discussed.
从时间相关的角度使用高斯波包研究了势垒上方的量子反射现象。过渡路径时间分布（原则上可以通过实验测量）用于研究与反射和势垒透射相关的平均飞行时间 ⟨t⟩和 ⟨t⟩，特别关注它们对势垒宽度的依赖性。这两个飞行时间及其差值 Δt 都表现出两种不同的状态，这取决于入射波包的空间宽度与势垒长度的比值。当比值大于 1 时，反射和传输动力学是相干的，并且由势垒上方的共振主导。飞行时间 ⟨t⟩和飞行时间差值 Δt 随势垒宽度（几乎与透射概率同相）而振荡。这些振荡反映了与反射和透射波相干叠加相关的动量滤波效应。对于比值小于 1 的情况，势垒反射和传输动力学是非相干的，并且没有振荡。通过分析确定了分离相干和非相干状态的势垒宽度。在相干状态下，当考虑反射和传输的魏格纳相位时间延迟时，时间差 Δt 作为势垒宽度的函数的振荡结构是不存在的。我们得出的结论是，魏格纳相位时间不能正确描述势垒上方反射的时间特性。我们还发现，反射和透射波包的结构取决于过程的相干性。在相干状态下，波包可能具有重叠的峰值结构，但峰值未完全分辨。在非相干状态下，波包在时间上分裂成明显分离的高斯样波，每个波包都反映了波包在退出之前穿过势垒区域的次数。在非相干状态下，使用经典轨迹的经典魏格纳近似，当经典轨迹到达势垒的边缘时，就像势垒是一个阶跃势一样被反射或透射，在定量上是合理的。讨论了在共振反应散射中观察到的相干性的影响。
